We report the discovery of a bright X-ray transient, CXOU J132527.6-430023, in the nearby early-type galaxy NGC 5128. The source was first detected over the course of five Chandra observations in 2007, reaching an unabsorbed outburst luminosity of 1-2*10^38 erg/s in the 0.5-7.0 keV band before returning to quiescence. Such luminosities are possible for both stellar-mass black hole and neutron star X-ray binary transients. Here, we attempt to characterize the nature of the compact object. No counterpart has been detected in the optical or radio sky, but the proximity of the source to the dust lanes allows for the possibility of an obscured companion. The brightness of the source after a >100 fold increase in X-ray flux makes it either the first confirmed transient non-ULX black hole system in outburst to be subject to detailed spectral modeling outside the Local Group, or a bright (>10^38 erg/s) transient neutron star X-ray binary, which are very rare. Such a large increase in flux would appear to lend weight to the view that this is a black hole transient. X-ray spectral fitting of an absorbed power law yielded unphysical photon indices, while the parameters of the best-fit absorbed disc blackbody model are typical of an accreting ~10 Msol black hole in the thermally dominant state. ; Comment: 8 pages, 6 figures, accepted for publication in ApJ